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Elastic–plastic behavior of a semicircular frame being pressed against a rigid plane

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Abstract

As a simplified structural model, a semicircular frame is used to study the crashworthiness behavior of an aircraft fuselage. The quasi-static large elastic–plastic deformation of a semicircular frame in the process of its being pressed against a rigid ground is analyzed. First, based on the linear elastic assumption, the quasi-static large deformation contact process of the frame can be divided into three phases, i.e., point contact, line contact and post-buckling. By means of a shooting method, the relations between the displacement and contact force as well as the distribution of bending moment in the three phases are obtained. Then, by assuming an elastic, perfectly-plastic moment–curvature relationship for the semi-circular frame, the contact process is analyzed in detail to reveal the plastic collapse mechanism, the traveling of plastic hinge and the force–displacement relationship. In order to verify the analysis, a preliminary experiment was conducted, in which two types of half rings with clamped ends were pressed by a rigid plate. In addition, a numerical simulation is also conducted by employing ABAQUS to analyze both rectangular cross-sectional beam and I-beam. Finally, the theoretical predictions are compared with the experimental results and numerical solutions, showing that the elastic–plastic analysis can predict the contact process very well.

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Abbreviations

H, H1, H2:

distances between rigid plate and the center of semicircular frame

R0, R:

initial and local radius of curvature of the curved beam

S :

arc length of the curve beam

F, G:

horizontal and vertical forces

B :

half length of the contact area

M0, M r , M x :

bending moments at contact point, right end and the maximum value near the middle of the quadrant arc

Me, Mp:

fully elastic and plastic bending moments

F cr :

buckling force

W :

mass of the semicircular frame

E :

Young’s modulus

h, h1, h2:

non-dimensional quantities of H, H 1, H 2

hp1, hp2, hp3:

non-dimensional distance of the rigid plate from the frame center during elastic plastic contact

δ :

non-dimensional displacement of the plate after initial contact

κ, κp :

initial and yielding curvature of the curved beam

t :

thickness of rectangular beam, wall-thickness of I-beam

b :

non-dimensional half length of the contact area

s :

non-dimensional arc length

x, y:

non-dimensional horizontal and vertical coordinates

θ :

inclination of the arc with respect to the x direction

β :

inclination of the resultant force of F and G

f,g:

non-dimensional quantities of F and G

f cr :

non-dimensional buckling force

σ Y :

yield stress

me, mp:

non-dimensional fully elastic and plastic bending moments

m0, m r , m x :

non-dimensional quantities of M 0, M r , M x

b w ,h w :

width and height of a general beam

e a :

non-dimensional energy dissipation

e s :

specific energy absorption

p, p m :

non-dimensional contact force and mean contact force for a half ring

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Authors and Affiliations

  1. Institute of Solid Mechanics, Beihang University, Beijing, 100083, China

    X. W. Zhang & J. L. Yang

  2. Department of Mechanical Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong, China

    X. W. Zhang & T. X. Yu

Authors
  1. X. W. Zhang
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  2. J. L. Yang
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  3. T. X. Yu
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Corresponding author

Correspondence to J. L. Yang.

Additional information

The project supported by the National Natural Science Foundation of China (10532020).

The English text was polished by Keren Wang.

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Zhang, X.W., Yang, J.L. & Yu, T.X. Elastic–plastic behavior of a semicircular frame being pressed against a rigid plane. Acta Mech Sin 24, 419–432 (2008). https://doi.org/10.1007/s10409-008-0150-5

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  • DOI: https://doi.org/10.1007/s10409-008-0150-5

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